Abstract: This paper deals with the analysis of plane and axisymmetric problems with concrete-like material behavior where the weak tensile strength and crushing and cracking behavior are considered. The concrete is treated as a linear elastic, plastic, strain-hardening, and fracture material. The stress-strain relations are first stated in matrix form for the general case of three-dimensional stress states and then reduced to the special cases of plane stress, plane strain, and axisymmetric stress conditions, suitable for use in finite element analysis. The numerical analysis is obtained within the framework of the finite element method and a step- by-step integration procedure. The method is applied to the punch-indentation problems of concrete and metal blocks under plane strain conditions. Comparisons between analysis and experiment are made.